Here is a tutorial for setting up a demonstration for the Least-Squares Regression for your MDM 4U class.
Go to Graph -> Grid Form -> Square Grid to establish a grid then select and drag an axis until your origin is toward the bottom left corner.
Create a scattering of points on your grid with the point tool. I am making mine spread out a bit to leave room for a possible line of best fit.
Next you can create a line or ray using the appropriate tool. You can find the tool by clicking and holding on line segment
Okay, here's the fun part: create a series of perpendicular lines. Select a point and the x-axis then go to Construct -> perpendicular line. Do this for each point.
Next, select a vertical line and the line of best fit and go to Construct Midpoint. Do this for each vertical line.
In order to create squares here, we need to measure appropriately the length of the segments between the line of best fit and the points. Use circles to measure the lengths. Draw circles from the point to the line of best fit.
Use the line segment tool to create perpendicular radii as shown below. Hold down shift while constructing the line segment to guarantee horizontality.
Use circles again to find the last corner of the square. Select the point which will be the center of your circle followed by the line segment which will be the radius of your circle-then go to Construct -> Circle by Center+Radius. Again, do this for each point.
Create line segments as shown by holding shift while constructing.
Okay, super-duper-math-pun-time! COMPLETE THE SQUARE!
Clean up time. Select all the vertical lines and circles you created and go to Display -> Hide Objects (ctrl h is your friend here)
Yeah okay I forgot a whole side of the square. May as well do this now. So much for my complete the square joke.
Select all the sides of your squares and go to Display -> Line Width -> Dashed for the nice effect.
Select all the points you don't need and hide them (ctrl h) and select the line of best fit to give it a colour change and thick line.
Now you have a fully functioning least squares residuals demo to use. Move the line around and alter its direction to change the squares.